Finance Test 2

3. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. What is the value of each call option? A. $1.6 B. $2.0 C. $2.4 D. $3.0

A. $1.6

13. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European put option on the stock with a strike price of $32 that expires in 6 months with u = 1.1 and d = 0.9. Each step is 3 months, the risk free rate is 8%. A. $2.24 B. $2.44 C. $2.64 D. $2.84

A. $2.24

A trader buys a call and sells a put with the same strike price and maturity date. What is the position equivalent to?A) A long forward B) A short forward C) Buying the asset D) None of the above

A. A long forward

Which of the following is an example of an option class?A) All calls on a certain stock B) All calls with a particular strike price on a certain stock C) All calls with a particular time to maturity on a certain stock D) All calls with a particular time to maturity and strike price on a certain stock

A. All calls on a certain stock

Which of the following is NOT true?A) An American put option is always worth less than the present value of the strike price B) A European put option is always worth less than the present value of the strike price C) A European call option is always worth less than the stock price D) An American call option is always worth less than the stock price

A. An American put option is always worth less than the present value of the strike price

When volatility increases with all else remaining the same, which of the following is true? A) Both calls and puts increase in value B) Both calls and puts decrease in value C) Calls increase in value while puts decrease in value D) Puts increase in value while calls decrease in value

A. Both calls and puts increase in value

6. Which of the following describes how American options can be valued using a binomial tree? A. Check whether early exercise is optimal at all nodes where the option is in-the-money B. Check whether early exercise is optimal at the final nodes C. Check whether early exercise is optimal at the penultimate nodes and the final nodes D. None of the above

A. Check whether early exercise is optimal at all nodes where the option is in-the-money

Which of the following is true for American options?A) Put-call parity provides an upper and lower bound for the difference between call and put prices B) Put call parity provides an upper bound but no lower bound for the difference between call and put prices C) Put call parity provides an lower bound but no upper bound for the difference between call and put prices D) There are no put-call parity results

A. Put-call parity provides an upper and lower bound for the difference between call and put prices

An investor has exchange-traded put options to sell 100 shares for $20. There is a $1 cash dividend. Which of the following is then the position of the investor?A) The investor has put options to sell 100 shares for $20 B) The investor has put options to sell 100 shares for $19 C) The investor has put options to sell 105 shares for $19 D) The investor has put options to sell 105 shares for $19.05

A. The investor has put options to sell 100 shares for $20

When a six-month option is purchased.... A) The price must be paid in full B) Up to 25% of the option price can be borrowed using a margin account C) Up to 50% of the option price can be borrowed using a margin account D) Up to 75% of the option price can be borrowed using a margin account

A. The price must be paid in full

Which of the following describes a call option? A) The right to buy an asset for a certain price B) The obligation to buy an asset for a certain price C) The right to sell an asset for a certain price D) The obligation to sell an asset for a certain price

A. The right to buy an asset for a certain price

Which of the following must post margin?A) The seller of an option B) The buyer of an option C) The seller and the buyer of an option D) Neither the seller nor the buyer of an option

A. The seller of an option

Which of the following best describes the intrinsic value of an option? A) The value it would have if the owner were forced to exercise immediately B) The Black-Scholes-Merton price of the option C) The lower bound for the option's price D) The amount paid for the option

A. The value it would have if the owner were forced to exercise immediately

12. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when u = 1.1 and d = 0.9. A. $1.29 B. $1.49 C. $1.69 D. $1.89

B. $1.49

17. The current price of a non-dividend paying stock is $50. Use a two-step tree to value an American put option on the stock with a strike price of $48 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 20%. Which of the following is the option price? A. $1.95 B. $2.00 C. $2.05 D. $2.10

B. $2.00

A stock price (which pays no dividends) is $50 and the strike price of a two year European put option is $54. The risk-free rate is 3% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound . A) $5.00 B) $5.98 C) $4.98 D) $3.98

B. $5.98

16. If the volatility of a non-dividend-paying stock is 20% per annum and a risk-free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter p for a tree with a three-month time step? A. 0.50 B. 0.54 C. 0.58 D. 0.62

B. 0.54

Which of the following is true?A) An American call option on a stock should never be exercised early B) An American call option on a stock should never be exercised early when no dividends are expected C) There is always some chance that an American call option on a stock will be exercised early D) There is always some chance that an American call option on a stock will be exercised early when no dividends are expected

B. An American call option on a stock should never be exercised early when no dividends are expected

1. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. Which of the following hedges the position? A. Buy 0.6 shares for each call option sold B. Buy 0.4 shares for each call option sold C. Short 0.6 shares for each call option sold D. Short 0.6 shares for each call option sold

B. Buy 0.4 shares for each call option sold

Which of the following can be used to create a long position in a European put option on a stock?A) Buy a call option on the stock and buy the stock B) Buy a call on the stock and short the stock C) Sell a call option on the stock and buy the stock D) Sell a call option on the stock and sell the stock

B. Buy a call on the stock and short the stock

14. Which of the following is NOT true in a risk-neutral world? A. The expected return on a call option is independent of its strike price B. Investors expect higher returns to compensate for higher risk C. The expected return on a stock is the risk-free rate D. The discount rate used for the expected payoff on an option is the risk-free rate

B. Investors expect higher returns to compensate for higher risk

Which of the following is NOT traded by the CBOE?A) Weeklys B) Monthlys C) Binary options D) DOOM options

B. Monthlys

Which of the following is true when dividends are expected?A) Put-call parity does not hold B) The basic put-call parity formula can be adjusted by subtracting the present value of expected dividends from the stock price C) The basic put-call parity formula can be adjusted by adding the present value of expected dividends to the stock price D) The basic put-call parity formula can be adjusted by subtracting the dividend yield from the interest rate

B. The basic put-call parity formula can be adjusted by subtracting the present value of expected dividends from the stock price

Which of the following describes a difference between a warrant and an exchange-traded stock option?A) In a warrant issue, someone has guaranteed the performance of the option seller in the event that the option is exercised B) The number of warrants is fixed whereas the number of exchange-traded options in existence depends on trading C) Exchange-traded stock options have a strike price D) Warrants cannot be traded after they have been purchased

B. The number of warrants is fixed whereas the number of exchange-traded options in existence depends on trading

In which of the following cases is an asset NOT considered constructively sold?A) The owner shorts the asset B) The owner buys an in-the-money put option on the asset C) The owner shorts a forward contract on the asset D) The owner shorts a futures contract on the stock

B. The owner buys an in-the-money put option on the asset

The price of a European call option on a stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. A dividend of $1 is expected in six months. What is the price of a one-year European put option on the stock with a strike price of $50? A) $8.97 B) $6.97 C) $3.06 D) $1.12

C. $3.06

2. The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. What is the risk-neutral probability of that the stock price will be $36? A. 0.6 B. 0.5 C. 0.4 D. 0.3

C. 0.4

11. Which of the following are NOT true A. Risk-neutral valuation and no-arbitrage arguments give the same option prices B. Risk-neutral valuation involves assuming that the expected return is the risk-free rate and then discounting expected payoffs at the risk-free rate C. A hedge set up to value an option does not need to be changed D. All of the above

C. A hedge set up to value an option does not need to be changed

Which of the following describes a long position in an option?A) A position where there is more than one year to maturity B) A position where there is more than five years to maturity C) A position where an option has been purchased D) A position that has been held for a long time

C. A position where an option has been purchased

4. The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. Which of the following is necessary to hedge the position? A. Buy 0.2 shares for each option purchased B. Sell 0.2 shares for each option purchased C. Buy 0.8 shares for each option purchased D. Sell 0.8 shares for each option purchased

C. Buy 0.8 shares for each option purchased

When interest rates increase with all else remaining the same, which of the following is true? A) Both calls and puts increase in value B) Both calls and puts decrease in value C) Calls increase in value while puts decrease in value D) Puts increase in value while calls decrease in value

C. Calls increase in value while puts decrease in value

When the stock price increases with all else remaining the same, which of the following is true? A) Both calls and puts increase in value B) Both calls and puts decrease in value C) Calls increase in value while puts decrease in value D) Puts increase in value while calls decrease in value

C. Calls increase in value while puts decrease in value

Which of the following describes LEAPS?A) Options which are partly American and partly European B) Options where the strike price changes through time C) Exchange-traded stock options with longer lives than regular exchange-traded stock options D) Options on the average stock price during a period of time

C. Exchange-traded stock options with longer lives than regular exchange-traded stock options

The price of a stock is $67. A trader sells 5 put option contracts on the stock with a strike price of $70 when the option price is $4. The options are exercised when the stock price is $69. What is the trader's net profit or loss?A) Loss of $1,500 B) Loss of $500 C) Gain of $1,500 D) Loss of $1,000

C. Gain of $1,500

An investor has exchange-traded put options to sell 100 shares for $20. There is a 2 for 1 stock split. Which of the following is the position of the investor after the stock split?A) Put options to sell 100 shares for $20 B) Put options to sell 100 shares for $10 C) Put options to sell 200 shares for $10 D) Put options to sell 200 shares for $20

C. Put options to sell 200 shares for $10

Which of the following are true for CBOE stock options?A) There are no margin requirements B) The initial margin and maintenance margin are determined by formulas and are equal C) The initial margin and maintenance margin are determined by formulas and are different D) The maintenance margin is usually about 75% of the initial margin

C. The initial margin and maintenance margin are determined by formulas and are equal

20. A tree is constructed to value an option on an index which is currently worth 100 and has a volatility of 25%. The index provides a dividend yield of 2%. Another tree is constructed to value an option on a non-dividend-paying stock which is currently worth 100 and has a volatility of 25%. Which of the following are true? A. The parameters p and u are the same for both trees B. The parameter p is the same for both trees but u is not C. The parameter u is the same for both trees but p is not D. None of the above

C. The parameter u is the same for both trees but p is not

A European call and a European put on a stock have the same strike price and time to maturity. At 10:00am on a certain day, the price of the call is $3 and the price of the put is $4. At 10:01am news reaches the market that has no effect on the stock price or interest rates, but increases volatilities. As a result the price of the call changes to $4.50. Which of the following is correct?A) The put price increases to $6.00 B) The put price decreases to $2.00 C) The put price increases to $5.50 D) It is possible that there is no effect on the price

C. The put price increases to $5.50

18. Which of the following describes delta? A. The ratio of the option price to the stock price B. The ratio of the stock price to the option price C. The ratio of a change in the option price to the corresponding change in the stock price D. The ratio of a change in the stock price to the corresponding change in the option price

C. The ratio of a change in the option price to the corresponding change in the stock price

7. In a binomial tree created to value an option on a stock, the expected return on stock is A. Zero B. The return required by the market C. The risk-free rate D. It is impossible to know without more information

C. The risk-free rate

8. In a binomial tree created to value an option on a stock, what is the expected return on the option? A. Zero B. The return required by the market C. The risk-free rate D. It is impossible to know without more information

C. The risk-free rate

Which of the following describes a situation where an American put option on a stock becomes more likely to be exercised early? A) Expected dividends increase B) Interest rates decrease C) The stock price volatility decreases D) All of the above

C. The stock price volatility decreases

A stock price (which pays no dividends) is $50 and the strike price of a two year European put option is $54. The risk-free rate is 3% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? A) $4.00 B) $3.86 C) $2.86 D) $0.86

D. $0.86

5. The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. What is the value of each option? The risk-free interest rate is 2% per annum with continuous compounding. A. $3.93 B. $2.93 C. $1.93 D. $0.93

D. $0.93

The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. What is the price of a one-year European put option on the stock with a strike price of $50? A) $9.91 B) $7.00 C) $6.00 D) $2.09

D. $2.09

15. If the volatility of a non-dividend paying stock is 20% per annum and a risk-free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter u for a tree with a three-month time step? A. 1.05 B. 1.07 C. 1.09 D. 1.11

D. 1.11

Which of the following describes a short position in an option?A) A position in an option lasting less than one month B) A position in an option lasting less than three months C) A position in an option lasting less than six months D) A position where an option has been sold

D. A position where an option has been sold

Which of the following is an example of an option series?A) All calls on a certain stock B) All calls with a particular strike price on a certain stock C) All calls with a particular time to maturity on a certain stock D) All calls with a particular time to maturity and strike price on a certain stock

D. All calls with a particular time to maturity and strike price on a certain stock

10. Which of the following is true for a call option on a stock worth $50 A. As a stock's expected return increases the price of the option increases B. As a stock's expected return increases the price of the option decreases C. As a stock's expected return increases the price of the option might increase or decrease D. As a stock's expected return increases the price of the option on the stock stays the same

D. As a stock's expected return increases the price of the option on the stock stays the same

When the time to maturity increases with all else remaining the same, which of the following is true? A) European options always increase in value B) The value of European options either stays the same or increases C) There is no effect on European option values D) European options are liable to increase or decrease in value

D. European options are liable to increase or decrease in value

9. A stock is expected to return 10% when the risk-free rate is 4%. What is the correct discount rate to use for the expected payoff on an option in the real world? A. 4% B. 10% C. More than 10% D. It could be more or less than 10%

D. It could be more or less than 10%

Interest rates are zero. A European call with a strike price of $50 and a maturity of one year is worth $6. A European put with a strike price of $50 and a maturity of one year is worth $7. The current stock price is $49. Which of the following is true?A) The call price is high relative to the put price B) The put price is high relative to the call price C) Both the call and put must be mispriced D) None of the above

D. None of the above

Which of the following is true? A) A long call is the same as a short put B) A short call is the same as a long put C) A call on a stock plus a stock the same as a put D) None of the above

D. None of the above

Consider a put option and a call option with the same strike price and time to maturity. Which of the following is true?A) It is possible for both options to be in the money B) It is possible for both options to be out of the money C) One of the options must be in the money D) One of the options must be either in the money or at the money

D. One of the options must be either in the money or at the money

An investor has exchange-traded put options to sell 100 shares for $20. There is 25% stock dividend. Which of the following is the position of the investor after the stock dividend?A) Put options to sell 100 shares for $20 B) Put options to sell 75 shares for $25 C) Put options to sell 125 shares for $15 D) Put options to sell 125 shares for $16

D. Put options to sell 125 shares for $16

When dividends increases with all else remaining the same, which of the following is true?A) Both calls and puts increase in value B) Both calls and puts decrease in value C) Calls increase in value while puts decrease in value D) Puts increase in value while calls decrease in value

D. Puts increase in value while calls decrease in value

When the strike price increases with all else remaining the same, which of the following is true?A) Both calls and puts increase in value B) Both calls and puts decrease in value C) Calls increase in value while puts decrease in value D) Puts increase in value while calls decrease in value

D. Puts increase in value while calls decrease in value

Which of the following is the put-call parity result for a non-dividend-paying stock?A) The European put price plus the European call price must equal the stock price plus the present value of the strike price B) The European put price plus the present value of the strike price must equal the European call price plus the stock price C) The European put price plus the stock price must equal the European call price plus the strike price D) The European put price plus the stock price must equal the European call price plus the present value of the strike price

D. The European put price plus the stock price must equal the European call price plus the present value of the strike price

When moving from valuing an option on a non-dividend paying stock to an option on a currency which of the following is true? A. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate in all calculations B. The formula for u changes C. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate for discounting D. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate when p is calculated

D. The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate when p is calculated

The price of a stock is $64. A trader buys 1 put option contract on the stock with a strike price of $60 when the option price is $10. When does the trader make a profit?A) When the stock price is below $60 B) When the stock price is below $64 C) When the stock price is below $54 D) When the stock price is below $50

D. When the stock price is below $50